How do the volumes you calculated with the formula and with the cubic block method compare?

The roots of the given quadratic equation are x = -2/3 and x = -2.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is a quadratic equation as follows -

3x² + 7 = - 8x + 3

The given quadratic equations are -

3x² + 7 = - 8x + 3

3x² + 8x = 3 - 7

3x² + 8x + 4 = 0

(x + 2/3)(x + 2) = 0

(x + 2/3) = 0   and   (x + 2) = 0

x = -2/3   and   x = -2    

Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.

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The solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

The relationship between two values that are not equal is described by inequalities. Equal does not necessarily mean unequal. The "not equal symbol" is typically used to denote that two values are not equal.

Given:

1 / 2x < 6

x < 6 × 2

x < 12

Therefore, the solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.

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Answer:

2

Step-by-step explanation:

x + 2y = 14

2y = -x + 14

y = -1/2 x + 7

m = -1/2

product of slopes is -1

so perpendicular slope is 2

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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let's evaluate :

Answer:

e² + 4e + 3

Step-by-step explanation:

(e + 3)(e + 1)

Each term in the second factor is multiplied by each term in the first factor , that is

e(e + 1) + 3(e + 1) ← distribute parenthesis

= e² + e + 3e + 3 ← collect like terms

= e² + 4e + 3

Answer:$12$

Step-by-step explanation:

Answer:12.375

Step-by-step explanation:

Mutiply 4.5 x 2.75 and you'll get your answer.

The given critical point is unstable.

What is critical point?

A critical point could be a local maximum if the function changes from increasing to decreasing at that time, whereas it's known as a neighborhood minimum if the perform changes from decreasing to increasing at that time.

A purpose is associate degree inflection point if the concavity of the perform changes at that time.

Main body:

dx/dt=

dy/dt=y(0.5x-0.25)

Obviously, the right hand sides of these ODEs vanish when x = 0 and y = 0; and so (0, 0) is a critical point for the system. The coefficient matrix for the corresponding linearization is

\(\left[\begin{array}{ccc}d/dx(-x+y+2xy)&d/dy(-x+y+2xy)\\d/dx(y(0.5x-0.25)&d/dy(y(0.5x-0.25)\end{array}\right]\)

= \(\left[\begin{array}{ccc}-1+2y&1+2x\\0.5y&-0.25+0.5x\end{array}\right]\)

put x = 0 , y= 0

=\(\left[\begin{array}{ccc}-1&1\\0&-0.25\end{array}\right]\)

We have

det (A − λI) = (1+λ)(λ+0.25)

and so we have two real eigenvalues λ = -1 and λ= -0.25

A having two real eigenvalues of opposite

signs means the system has an unstable saddle point at (0, 0).

Hence it is unstable.

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(a) (i) 0.3174 = 31.74% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 317.

(b) (i) 0.0026 = 0.26% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 3.

(C) Reduces the process standard deviation and causes no change in the number of defects.

When the distribution is normal, we use the z-score formula.

In a set with mean  and standard deviation, the score of a measure X is given by:

         Z = X-μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

We have that: μ = 10 and σ = 0.12

(i). Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

  Z = X-μ /σ

⇒ Z = 9.88 - 10/0.12

⇒ Z = -1, has a p-value of 0.1587

⇒ 2× 0.1587 = 0.3174

This means 0.3174 = 31.74% probability of a defect

(ii)  Calculate the expected number of defects for a 1,000-unit production run.

The expected number of defects is 31.74% of 1000. So

0.3174*1000 = 317.4

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 317.

Question (b):

The mean remains the same, but the standard deviation is now

(i) Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

   Z = X-μ /σ

⇒ Z = 9.88 -10/0.04

⇒ Z = -3

⇒ Z = -3, has a p-value of 0.0013

which means 2× 0.0013 = 0.0026

from which 0.0026 = 0.26% probability of a defect

(ii) Calculate the expected number of defects for a 1,000-unit production run. The expected number of defects is 31.74% of 1000. Thus,

⇒ 0.0026*1000 = 2.6

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 3.

(C) The advantage of reducing process variation, thereby causing problem limits to be at a greater number of standard deviations from the mean Reduces the process standard deviation and causes no change in the number of defects.

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Including reaction time, the stopping distance is more than 20 feet at 10 miles per hour, at 20 miles per hour it will be about 63 feet.

The distance traveled while the driver sees a hazard and applies the brakes, as well as when the vehicle comes to a complete stop from its original speed, is included in the stopping distance.

We have:

Including reaction time, the stopping distance is more than 20 feet at 10 miles per hour

In this case, the stopping distance will be about 63 feet if the stopping distance is more than 20 feet at 10 miles per hour.

Thus, the including reaction time, the stopping distance is more than 20 feet at 10 miles per hour, at 20 miles per hour it will be about 63 feet.

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Answer:

What percent of the bill would an $11 tip be?: 22%

What percent of the bill would a $12.50 tip be? 25%

Step-by-step explanation:

Edegunity

Answer:

1. 22%

2. 25%

Step-by-step explanation:

edginuity

We can represent "f(x)" as:

The derivate of a monomial we multiply the monomial by its expoent and subtract one on the expoent. We have:

The correct option is "a".

Answer:

By angle sum property,

56 + 92 = 148

180 - 148 = 32

linear pair

so ,  180 - 32

= 148

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The range of the function f(x) = 2(3)x is best described by y > 0. Particularly the function when the constant is e, a function whose value is a constant raised to the power of the argument.

The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response. The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

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Answer:

34: yes

40: no

32: yes

35: no

Step-by-step explanation:

hope this helps!

Answer:

im sorry I wish I could help are there any other questions you have?

Step-by-step explanation:

Lyndon should spend $38.05 or more to get a free T-shirt.

We have to find the statement best represents all of the amounts he can spend to get a free T-shirt

Suppose that the amount Lyndon get free T shirt is x.

Given that a clothing store offers a free T-shirt when a customer spends $75 or more.

Lyndon has already spent $36.95.

\(x+36.95\geq 75\)

To find the value of x,

Solve above inequality

\(x\geq 75-36.95\)

\(x\geq 38.05\)

Therefore,

Lyndon should spend $38.05 or more to get a free T-shirt

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Answer:

Step-by-step explanation: the answer is 9 years

Answer:

10

Step-by-step explanation:

To find the number, divide 3 by 0.3

3/0.3

= 10

So, 30% of 10 is 3.

The fraud triangle is a model that describes the three key factors that must be present for fraud to occur: opportunity, rationalization, and pressure.

These factors are often represented as the three sides of a triangle, with fraud being the result at the center.

Opportunity refers to the ability of an individual to commit fraud, either due to a lack of internal controls or the ability to override existing controls. Rationalization refers to the mental process by which an individual justifies the fraudulent behavior to themselves, often by convincing themselves that it is not really wrong or that they have a valid reason for doing it. Pressure refers to the external factors that motivate an individual to commit fraud, such as financial difficulties, job insecurity, or a desire to meet performance targets.

In summary, the fraud triangle indicates that all three conditions of opportunity, rationalization, and pressure must be present for fraud to be perpetrated.

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Answer:

1. 5xy^3

2.  4/9m^6 n^4

3. 2a^2/c

4. 4x^3m+6/3

Step-by-step explanation:

0,4

is where it would land and you can

Answer: 6

Step-by-step explanation:

The sentence "If it is a dog (d), it has fleas (f)" can be represented in symbolic form as d → f.

In symbolic logic, we represent the components of a sentence using letters or symbols. In this case, the given sentence has two components: "it is a dog" and "it has fleas." To represent these components, we assign the letter 'd' to "it is a dog" and the letter 'f' to "it has fleas."

The sentence "If it is a dog, it has fleas" implies a conditional relationship between the two components. It states that if something is a dog (d), then it has fleas (f). This can be symbolically represented as d → f, where the arrow (→) denotes the conditional relationship.

The given sentence, "If it is a dog (d), it has fleas (f)," can be represented in symbolic form as d → f. The arrow (→) in symbolic logic represents the conditional relationship. It indicates that if something is a dog (d), then it has fleas (f). In this symbolic representation, 'd' stands for "it is a dog," and 'f' represents "it has fleas."

The sentence is a conditional statement because it presents a hypothetical relationship between the two components. The truth value of the sentence depends on whether the antecedent (d) is true or false. If something is indeed a dog, then it implies that it has fleas. However, if it is not a dog, the statement does not make any specific claim about fleas.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

\(\frac{x}{x+2} - \frac{4}{x-2}=1\\or, \frac{x(x-2)}{(x+2)(x-2)} -\frac{4(x+2)}{(x+2)(x-2)}=1\\or, \frac{x^2-2x}{x^2-4} -\frac{(4x+8)}{x^2-4} =1\\or, \frac{x^2-2x-(4x+8)}{x^2-4} =1\\or, \frac{x^2-2x-4x-8}{x^2-4}=1\\or, {x^2-6x-8} =x^2-4\\or, -6x-8=-4\\or, 3x+4=2\\or, 3x = -2\\or, x =\frac{-2}{3}\)